Heisenberg Uncertainty Principle states that it is impossible to define what time and where an electron is and where is it going next. This makes it impossible to know exactly where an electron is traveling in an atom.

Since it is impossible to know where an electron is at a certain time, a series of calculations are used to approximate the volume and time in which the electron can be located. These regions are called Atomic Orbitals. These are also known as the quantum states of the electrons.

Only two electrons can occupy one orbital and they must have different spin states, ½ spin and ½ spin (easily visualized as opposite spin states).

Orbitals are grouped into subshells.

This field of study is called quantum mechanics.

3Atomic Subshells

These are some examples of atomic orbitals

S subshell (Spherical shape) There is one S orbital in an s subshell. The electrons can be located anywhere within the sphere centered at the atoms nucleus.

http//www.chm.davidson.edu/ronutt/che115/AO.htm

P Orbitals (Shaped like two balloons tied together) There are 3 orbitals in a p subshell that are denoted as px, py, and pz orbitals. These are higher in energy than the corresponding s orbitals.

D Orbitals The d subshell is divided into 5 orbitals (dxy, dxz, dyz, dz2 and dx2-y2). These orbitals have a very complex shape and are higher in energy than the s and p orbitals.

5Molecular Orbital Theory

The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations.

6Forming a Covalent Bond

Molecules can form bonds by sharing electron

Two shared electrons form a single bond

Atoms can share one, two or three pairs of electrons

forming single, double and triple bonds

Other types of bonds are formed by charged atoms (ionic) and metal atoms (metallic).

7Atomic and Molecular Orbitals (contd)

Orbital Mixing

When atoms share electrons to form a bond, their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they must

Have similar energy levels.

Overlap well.

Be close together.

This is and example of orbital mixing. The two atoms share one electron each from there outer shell. In this case both 1s orbitals overlap and share their valence electrons.http//library.thinkquest.org/27819/ch2_2.shtml 8Energy Diagram of Sigma Bond Formation by Orbital Overlap 9sp3 Hybrid atomic orbitals 10sp2 Hybrid atomic orbitals 11sp Hybrid atomic orbitals 12Multiple bonds with VB 13Multiple bonds with VB 14Molecular Orbital Theory

Each line in the diagram represents an orbital.

The molecular orbital volume encompasses the whole molecule.

The electrons fill the molecular orbitals of molecules like electrons fill atomic orbitals in atoms

15Molecular Orbital Theory

Electrons go into the lowest energy orbital available to form lowest potential energy for the molecule.

The maximum number of electrons in each molecular orbital is two. (Pauli exclusion principle)

One electron goes into orbitals of equal energy, with parallel spin, before they begin to pair up. (Hund's Rule.)

16Diatomic Molecular Orbital Theory

In the case of diatomic molecules, the interactions are easy to see and may be thought of as arising from the constructive interference of the electron waves (orbitals) on two different atoms, producing a bonding molecular orbital, and the destructive interference of the electron waves, producing an antibonding molecular orbital

This Approach is called LCAO-MO

(Linear Combination of Atomic Orbitals to Produce Molecular Orbitals)

A Little Math is need to understand Only a Little I promise! 17Atomic and Molecular Orbitals

In atoms, electrons occupy atomic orbitals, but in molecules they occupy similar molecular orbitals which surround the molecule.

The two 1s atomic orbitals combine to form two molecular orbitals, one bonding (s) and one antibonding (s).

This is an illustration of molecular orbital diagram of H2.

Notice that one electron from each atom is being shared to form a covalent bond. This is an example of orbital mixing.

FHHF 28Molecular Orbitals in HFThis non-bonding molecular orbital (n) has an almost spherical lobe showing only slight delocalisation between the two nuclei. Non-bonding orbitals look only slightly different to atomic orbitals, and have almost the same energy.2p1s

n

2sThis core orbital is almost unchanged from the F 1s orbital. The electrons are bound tightly to the F nucleus.n

H F FHHF 29Molecular Orbitals in HFThis (empty) LUMO is an antibonding orbital with a node on the interatomic axis between H and F.These two degenerate (filled) HOMOs are centred on the F atom, like 2px and 2py orbitals.s2p1s

nn

s

n

Electrons in these two orbitals are not shared (much) by the fluorine nucleus. They behave like the 2p orbitals and are also non-bonding (n).This MO, which is is like a 2pz orbital, is lower in energy in the molecule (a bonding orbital), and one lobe is delocalised around the H atom.n

FHHF 30Molecular Orbital Diagram (CH4)

So far, we have only look at molecules with two atoms. MO diagrams can also be used for larger molecules.

http//www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html 31Molecular Orbital Diagram (H2O) 32Molecular Orbital TheoryDiatomic molecules The bonding in F2The second set of combinations with ? symmetry (orthogonal to the first set)This produces an MO over the molecule with a node on the bond between the F atoms. This is thus a bonding MO of ?u symmetry.

?2pxA2pxB?u ? 0.5 (2pxA 2pxB)This produces an MO around both F atoms that has two nodes one on the bond axis and one perpendicular to the bond. This is thus an antibonding MO of ?g symmetry.-?2pxA2pxB?g ? 0.5 (2pxA - 2pxB) 33Molecular Orbital TheoryMO diagram for F2FFF23?u1?g2p(px,py)pz2p1?uEnergy3?g2?u2s2s2?g 34Molecular Orbital TheoryMO diagram for F2FFF2Another key feature of such diagrams is that the ?-type MOs formed by the combinations of the px and py orbitals make degenerate sets (i.e. they are identical in energy). The highest occupied molecular orbitals (HOMOs) are the 1?g pair - these correspond to some of the lone pair orbitals in the molecule and this is where F2 will react as an electron donor. The lowest unoccupied molecular orbital (LUMO) is the 3?u orbital - this is where F2 will react as an electron acceptor.3?uLUMO1?gHOMO2p(px,py)pz2p1?uEnergy3?g2?u2s2s2?g 35Molecular Orbital TheoryMO diagram for B2In the MO diagram for B2, there several differences from that of F2. Most importantly, the ordering of the orbitals is changed because of mixing between the 2s and 2pz orbitals. From Quantum mechanics the closer in energy a given set of orbitals of the same symmetry, the larger the amount of mixing that will happen between them. This mixing changes the energies of the MOs that are produced. The highest occupied molecular orbitals (HOMOs) are the 1?u pair. Because the pair of orbitals is degenerate and there are only two electrons to fill, them, each MO is filled by only one electron - remember Hunds rule. Sometimes orbitals that are only half-filled are called singly-occupied molecular orbtials (SOMOs). Since there are two unpaired electrons, B2 is a paramagnetic (triplet) molecule.BBB23?u1?g2p(px,py)pz2p3?gLUMOEnergy1?uHOMO2?u2s2s2?g 36Molecular Orbital TheoryDiatomic molecules MO diagrams for Li2 to F2 Remember that the separation between the ns and np orbitals increases with increasing atomic number. This means that as we go across the 2nd row of the periodic table, the amount of mixing decreases until there is no longer enough mixing to affect the ordering this happens at O2. At O2 the ordering of the 3?g and the 1?u MOs changes. As we go to increasing atomic number, the effective nuclear charge (and electronegativity) of the atoms increases. This is why the energies of the analogous orbitals decrease from Li2 to F2. The trends in bond lengths and energies can be understood from the size of each atom, the bond order and by examining the orbitals that are filled.In this diagram, the labels are for the valence shell only - they ignore the 1s shell. They should really start at 2?g and 2?u. 37More complicated molecules 38Modern MO calculationsW. Kohn (1923-)J. A. Pople (1925-2004)Nobel prize in Chemistry 1998 39Conclusions

Bonding electrons are localized between atoms (or are lone pairs).

Atomic orbitals overlap to form bonds.

Two electrons of opposite spin can occupy the overlapping orbitals.

Bonding increases the probability of finding electrons in between atoms.

It is also possible for atoms to form ionic and metallic bonds.

40References

http//www.chemguide.co.uk/atoms/properties/atomorbs.html

http//www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html

http//en.wikipedia.org/wiki/Molecular_orbital_theory

http//library.thinkquest.org/27819/ch2_2.shtml

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